Why are bones not connected both in rest and pose position?
Actually, when you are in Pose mode, the Rest Position put the bones at the same positions as in Edit mode. If you switch back to Pose Position you'll let all the Bone Constraints (and perhaps keyframes) act on your bones.

In your case, why, in Pose Position, is the calf bone in another position than in Edit mode (or Rest Position)? Because it has an IK Constraint and you can see the influence of this constraint, it will make the bone stick to its target, which is called "leg_ik.l".

So if you don't want your basic Pose mode to be this one, you need to stick your "leg_ik.l" to the tail of the calf (but in the process it will move some other bones so you will have to bring other corrections).